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A note on the number of S -Diophantine quadruples

Florian Luca, Volker Ziegler (2014)

Communications in Mathematics

Let ( a 1 , , a m ) be an m -tuple of positive, pairwise distinct integers. If for all 1 i < j m the prime divisors of a i a j + 1 come from the same fixed set S , then we call the m -tuple S -Diophantine. In this note we estimate the number of S -Diophantine quadruples in terms of | S | = r .

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